[ericandrews]

Hey there, simple question, regarding a PV diagram for a combustion engine, whats differene between isentropic expansion and adiabatic expansion ? Definitions say isentropic doesn't change in temp and entropy. Why not just call the expansion adiabatic ? (for an ideal combustion chamber)

[Donaldson Tan]

an adiabatic process is one whereby there is no transfer of heat between the system and its surroundings, thus Q (heat) = 0

an isoentropic process is one whereby entropy remains constant. if a process is both adiabatic and reversible, then it is considered as isoentropic.

adiabatic expansion can occur in a well-insulated system. neglecting kinetic energy, electrical energy, etc, drop in enthalpy of the system is effectively converted to work. an adiabatic expanion is thus considered to be most expanion. (dH = Q + W, where Q = 0) even in an ideal engine, it's not 100% efficient. this is well-demonstrated in Carnot'e engine.

[ppithermo]

An isentropic expansion is a  process which is both reversible and adiabatic. The entropy of the system remains constant.

An adiabatic expansion is a process where the system does not exchange heat with its envrironment. But in general, it is irreversible.

As a consequence of an irreversible expansion, the entropy of the adaibatic system increases.

[Juan R.]

almost all textbooks work just with the elementary equilibrium formulation for closed systems.

In general, from nonequilbrium thermodynamics

dS = d_iS + dQ_open/T + d_matterS

The last term accounts the transfer of matter with exterior and d_iS is the production of entropy due to irreversible phenomena. The form of production term is standard and known by decades: the product of thermodynamic flows J by thermodynamic forces F or affinities, d_iS = Sum F·J.

The mass term which does not appear in standard textbooks is easily understood. Take a flask with 50 mL of water at T, it has entropy S. Now add 50 mL of water also at T. The variation of heat (dQ) is zero and T is constant but variation of entropy is NOT zero because entropy is extensive magnitude and now the 100 mL system has entropy 2 S. The usual expression dS = dQ/T appears in textbooks is only valid for closed systems.

When one works with a closed system

dS = d_iS + dQ/T

since production of entropy is nonnegative. Many textbooks write above expression like

dS >= dQ/T

but if one want compute explicitely the production of entropy one may use the equation instead of the inequality.

For reversible processes, the production is zero

dS = dQ/T

and for adiabatic processes

dS = 0

Therefore, any isentropic process is an adiabatic and reversible process on a closed system.